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All of Simon's Comments + Replies

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

There’s a general consensus that, although quantum theory has changed our understanding of reality, Newtonian physics remains a reliable short term guide to the macro world. In principle, the vast majority of macro events that are just about to happen are thought to be 99.9999% inevitable, as opposed to 100% like Newton thought. From that I deduce that if a coin is shortly to be flipped, the outcome is unknown but, is as good as determined as makes no odds. Whereas if a coin is flipped farth... (read more)

1dadadarren3y

If I am understanding correctly, you are saying if the sleeping beauty problem does not use a coin toss, but measures the spin of an election instead, then the answer would be different. For the coin's case, you will give the probability of Heads (yet to be tossed ) as 2/3 after learning it is Monday. But for the spin's case, or a quantum coin, the probability must be 1/2 after learning it is Monday as it is a quantum event yet to happen. That seems very ad-hoc to me. And I think differentiating "true quantum randomness" with something "99.99999% inevitable" in probability theories is a huge can of worms. But anyway, my question is, if the sleeping beauty problem uses a quantum coin, what is the probability of heads when you wake up, before being told what day it is？ And what's your probability after learning "it is Monday now"? You said the answer depends on the quantum model used. I find it difficult to understand. Quantum models give different interpretations to make sense of the observed probability. The probability part is just experimental observation, not changed by which interpretation one prefers. But anyway, I am interested in your answer. How it can both keeps giving 1/2 to a quantum coin yet to be tossed, and obey bayesian probability when learning it is Monday. As for the clone and waking experiment, you said the answer depends on what happens after the experiment, whether or not there will be further awakenings: If there are, thirding; if not, halving. Again, very ad-hoc. If the awakening depends on a second coin to be tossed after the experiment ends, what then? How should an independent event in the future retroactively affect the probability of the first coin toss? What if both coins are quantum? How can you keep your answer bayesian? Just to be clear, my answer to cloning and waking P(H)=1/3 when waken up. The probability that I am the randomly chosen one, who would wake up regardless of the coin toss, is 2/3. The probability of Heads after le

1[comment deleted]3y

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

Well in that case, it narrows down what we agree about. Mathematical propositions aren’t events that happen. However, someone who doesn’t know a specific digit of Pi would assign likelihood to it’s value with the same rules of probability as they would to an event they don’t know about. I define credence merely as someone’s rational estimate of what’s likely to be true, based on knowledge or ignorance. Credence has no reason to discriminate between the three types of reality I talke... (read more)

1dadadarren3y

There are quite a few points here I disagree with. Allow me to explain. As I said in the previous reply, a mathematical statement by itself doesn't have a probability of being right/wrong. It is the process under which someone makes or evaluates said statement that can have a probability attached to it. Maybe the experimenter picked a random number from 1 to 10000 and then check that digit of pi to determine whether to destroy or wake the copy in question. And he picked ten in this case. This process/circumstance enables us to assign a probability to it. Whereas in self-locating probabilities there is no process explaining where the "I" comes from. Also just because macrophysical objects do not exhibit quantum phenomena such as randomness does not mean the macro world is deterministic. So I would not say Lewisian halfer predicting a fair coin yet to be tossed has the probability of Heads of 2/3 is metaphysically problem-free. Furthermore, even if you bite the bullet here, there are problems of probability pumping and retro-causations. I will attach the thought experiment later. Before going further, I wish to give PBR's answers to the thought experiment you raised. The probability that I am the clone or original is invalid. As it is a self-locating probability. The probability that today is Monday is 2/3. It is valid because both the clone and the original have the same value. There is no need to explain "which person I am". The probability that the chosen digit of pi falls between 6-0 is 2/3. It is valid for the same reason. And the probability that the coin landed heads given "I" am awake is invalid. i.e. we cannot update based on the information "I" am awake. As the value depends on if "I" am the clone or the original. I don't think thirders would have any trouble giving a probability of 2/3 to the tenth digit of pi. All they have to do is treat "I" as a random sample between the original and clone and then conduct the analysis from a god's eye perspective

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

Hi Dadarren. I haven’t forgotten our discussion and wanted to offer further food for thought. It might be helpful to explore definitions. As I see it, there are three kinds of reality about which someone can have knowledge or ignorance.

Contingent – an event in the world that is true or false based on whether it did or did not happen.

Analytic – a mathematical statement or expression that is true or false a priori.

Self-location – an identity or experience in space-time that is true or false at a given moment for an obser... (read more)

2dadadarren3y

For a, my opinion is while objectively there is no probability for the value of a specific digit of Pi, we can rightly say there is an attached probability in a specific context. For example, it is reasonable to ask why I am focusing on the tenth digit of Pi specifically? Maybe I just happen to memorize up to the ninth digit, and I am thinking about the immediate next one. Or maybe I just arbitartily choose the number 10. Anyway, there is a process leading to the focus of that particular digit. If that process does not contain any information about what that value is, then a principle of indifference is warranted. From a frequentist approach, we can think of repeating such processes and checking the selected digit, which can give a long-run relative frequency. For b, the probability is 1/2. It is valid because it is not a self-locating probability. Self-locating probability is about what is the first-person perspective in a given world, or the centered position of oneself in a possible world. But problem b is about different possible worlds. Another hint is the problem can be easily described without employing the subject's first-person perspective: what is the probability that the awakened person is the clone? Compare that to the self-locating probabilities we have been discussing: there are multiple agents and the one in question is specified by the first-person "I", which must be comprehended from the agent's perspective. From a frequentist approach, that experiment can be repeated many times and the long-run frequency would be 1/2. Both from the first-person perspective of the experiment subject, and from the perspective of any non-participating observers.

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

Ok that’s fine. I agree MWI is not proven. My point was only that it is the absolute self-location model. Those endorsing it propose the non-existence of probability, but still assign the mathematics of likelihood based on uncertainty from an observer. Forgive me for stumbling onto the implications of arguments you made elsewhere. I have read much of what you’ve written over time.

I especially agree that perspective disagreement can happen. That's what makes me a Halfer. Self-location&nb... (read more)

2dadadarren3y

But my explanation for perspective disagreement is based on the primitive nature of the first-person perspective. i.e. it cannot be explained therefore incommunicable. If we say there is A GOOD WAY to understand and explain it, and we must use assign self-locating probabilities this way, then why don't we explain our perspectives to each other as such, so we can have the exact same information and eliminate the disagreement? If we say the question has different sample spaces for different people, which is shown by repeating the experiment from their respective perspective gives different relative frequencies. Then why say when there is no relative frequency from a perspective there is still a valid probability? This is not self-consistent. To my knowledge, halfers have not provided a satisfactory explanation to perspective disagreement. Even though Katja Grace and John Pittard have pointed out for quite some time already. And if halfers want to use my explanation for the disagreement, and at the same time, reject my premises of primitive perspectives, then they are just putting assumptions over assumptions to preserve self-locating probability. To me, that's just because our nature of dislike saying "I don't know", even when there is no way to think about it. And what do halfers get by preserving self-locating probability? Nothing but paradoxes. Either we say there is a special rule of updating which keeps the double-halving instinct, or we update to 1/3. The former has been quite conclusively countered by Michael Titelbaum: as long as you assign a non-zero value to the probability to "today is Tuesday" it will result in paradoxes. The latter has to deal with Adam Elga's question from the paper which jump-started the whole debate: After knowing it is Monday, I will put a coin into your hand. You will toss it. The result determines whether you will be wake again tomorrow with a memory wipe. Are you really comfortable saying "I believe this is a fair coin and the

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

Ok here's some rebuttal. :) I don’t think it’s your communication that’s wrong. I believe it’s the actual concept. You once said that yours is a view that no-one else shares. This does not in itself make it wrong. I genuinely have an open mind to understand a new insight if I’m missing it. However I’ve examined this from many angles. I believe I understand what you’ve put forward.

In anthropic problems, issues of self-location and first person perspective lie at the heart. ... (read more)

2dadadarren3y

While there isn't anything wrong with your summarization of my position. I wouldn't call it an extrapolation. Instead, I think it is other camps like SSA and SIA that are doing the extrapolation. "I know I am this person but have no explanation or reason for it" seems right, and I stick to it in reasoning. In my opinion, it is SSA and SIA that try to use random sampling in an unrelated domain to give answers that do not exist. Which leads to paradoxes. I recognized my solution (PBR) as incompatible with MWI since the very beginning of forming my solution. I even explicitly wrote about it, right after the solution to anthropics on my website. The deeper reason is PBR actually has a different account of what scientific objective means. Self-locating probability is only the most obvious manifestation of this difference. I wrote about it in a previous post. Nonetheless, the source of probability is the most criticized point about MWI. "why does a bifurcating world with equal coefficients guarantee I would experience roughly the same frequencies? What forces the mapping between the "worlds" and my first-person experience?" Even avid MWI supporters like Sean Carrol regard this as the most telling criticism of MWI. And especially hard to answer. I would suggest not to deny PBR just because one likes MWI. Since nobody can be certain that MWI is the correct interpretation. Furthermore, there is no reason to be alarmed just because a solution of anthropics is connected with quantum interpretations. The two topics are connected, no matter which solution one prefers. For example, there is a series of debates between Darren Bradly and Alastair Wilson about whether or not SIA would naively confirm MWI. Regarding the disagreement between the adopted son and parents about being firstborn, I agree there is no probability to "I am a firstborn". There simply is no way to reason about it. The question is set up so that it is easy to substitute the question with "what is the pr

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y10

I’ll come back with a deeper debate in good time. Meanwhile I’ll point out one immediate anomaly.

I was genuinely unsure which position you’d take when you learnt the two envelopes were the same. I expected you to maintain there was no probability assigned to Envelope A. I didn’t expect you to invalidate probability for the contents of Envelope B. You argued this because any statement about the contents of Envelope B was now linked to your self-lo... (read more)

2dadadarren3y

Haha, that's OK. I admit I am not the best communicator nor anthropic an easy topic to explain. So I understand the frustration. But I really think my position is not complicated at all. I genuinely believe that. It just says take whatever the first-person perspective is as given, and don't come up with any assumptions to attempt explaining it. Also want to point out I didn't say P(B say Original) as invalid, I said P(P says Original|contents are the same) is invalid. Some of your sentencing seems to suggest the other way. Just want to clear that up. And I'm not playing any tricks. Remember Peter/Bob. I said the probability of Heads is 1/2, but you cannot update on the information that you have seen Peter? The reason being it involves using self-locating probability? It's the same argument here. There was a valid P(Heads) while no valid P(Heads|Peter). There is a valid P(B says Original) but no valid P(B says Original|Same) for the exact same reason. And You can't update the probability given you saw Bob either. But just because you are either going to see Peter or Bob, that does not mean P(Heads) is invalidated, just can't update on Peter/bob that's all. Similarly, just because envelopes are either "same" or "different", doesn't mean P(B says Orignal) is invalid. Just cannot update on either. And the coin toss and Envelop B are both random/unknown processes. So I am not trying to trick you. It's the same old argument. And by suggesting think of repeating experiments and counting the long-run frequencies, I didn't leave much to interpretation. If you imagine repeating the experiments as a first-person and can get a long-run frequency, then the probability is valid. If there is no long-run frequency unless you come up with some way to explain the first-person perspective, then there is no valid probability. You can deduce what my position says quite easily like that. There aren't any surprises. Anyway, I would still say arguing using concrete examples wi

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

I’ve allowed some time to digest on this occasion. Let's go with this example.

A clone of you is created when you’re asleep. Both of you are woken with identical memories. Under your pillow are two envelopes, call them A and B. You are told that inside Envelope A is the title ‘original’ or ‘copy’, reflecting your body’s status. Inside Envelope B is also one of those titles, but the selection was random and regardless of status. You are asked the likelihood that each enve... (read more)

2dadadarren3y

Here is the conclusion based on my positions: the probability of Original for Envelop A does not exist; probability of Original for Envelop B is 1/2; probability of Original for Envelop B given contents are the same does not exist. Just like previous thought experiments, it is invalid to update based on that information. Remember my position says first-person perspective is a primitive axiomatic fact? e.g. "I naturally know I am this particular person. But there is no reason or explanation for it. I just am." This means arguments that need to explain the first-person perspective, such as treating it as a random sample, are invalid. And the difference between Envelop A and B is that probability regarding B does not need to explain the first-person perspective, it can just use "I am this person" as given. My envelope's content is decided by a coin toss. While probability A needs to explain the first-person perspective (like treating it as a random sample.) Again this is easier seen with a frequentist approach. If you repeat the same clone experiment a lot of times and keep recording whether you are the Original of the Clone in each iteration. Then even as time goes on there is no reason for the relative fraction of "I am the Original" to converge to any particular value. Of course, we can count everyone from these experiments and the combined relative fraction would be 1/2. But without additional assumptions such as "I am a random sample from all copies." that is not the same as the long-run frequency for the first person. In contrast, I can repeat the cloning experiment many times, and the long-run frequency for Envelop B is going to converge to 1/2 for me, as it is the result of a fair coin toss. There is no need to explain why "I am this person" here. So from a first-person perspective, the probability for B describes my experience and is verifiable. While probability about A is not unless considering every copy together, which is not about the first-per

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

I doubt we’ll persuade each other :) As I understand it, in my example you’re saying that the moment a self-location is ruled out, any present and future updating is impossible – but the last known probability of the coin stands. So if Beauty rules out Heads/Peter and nothing else, she must update Heads from 1/2 to 1/3. Then if she subsequently rules out Tails/Peter, you say she can’t update, so she will stay with the last known valid probability of 1/3. On the other hand, if she ru... (read more)

1dadadarren3y

Let's not dive into another example right away. Something is amiss here. I never said anything about the order of getting the answers to "Is it Tails and Peter?" and "Is it Heads Peter?" would change the probability. I said we cannot update based on the negative answer of "Is it Tails Peter?" because it involves using self-locating probability. Whichever the order is, we can nevertheless update the probability of Heads to 1/3 when we get the negative answer to "Is it Heads and Peter?", because there is no self-locating probability involved here. But 1/3 is the correct probability only if Beauty did actually ask the question and get the negative response. I.E. There has to be a real question to update based on its answer. That does not mean Beauty would inevitably update P(Head) to 1/3 no matter what. Before Beauty opens her eyes, she could ask: "Is it Heads and Peter?". If she gets a positive answer then the probability of Heads would be 1. If she gets a negative answer the probability of Heads would update to 1/3. She could also ask "Is it Heads and Bob?". And the result would be the same. Positive answer: P(Head)=1, negative answer: P(Head)=1/3. So no matter which of the two symmetrical questions she is asking, she can only update her probability after getting the answer to it. I think we can agree on this. The argument saying my approach would always update P(Heads) to 1/3 no matter which person I see is as follows: first of all, no real question is asked, look at whether it is Peter or Bob. If I see Bob, then retroactively pose the question as "Is it Heads and Peter?" and get a negative answer. If I see Peter, then retroactively pose the question as "Is it Heads and Bob?" and get a negative answer. Playing the game like this would guarantee a negative answer no matter what. But clearly, you get the negative answer because you actively changing the question to look for it. We cannot update the probability this way. My entire solution is suggesting there i

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

Ok let’s see if we can pin this down! Either Beauty learns something relevant to the probability of the coin flip, or she doesn't. We can agree on this, even if you think updating can't happen with self-location.

Let’s go back to a straightforward version of the original problem. It's similar to one you came up with. If Heads there is one awakening, if Tails there are two. If Heads, it will be decided randomly whether she wakes on Monday or Tuesday. If Tails, she will be woken on both days w... (read more)

1dadadarren3y

Let me lay out the difference between my argument and yours, following your example. After learning the name/day of the week, halfer's probability is still 1/2. You said because something in both Heads and Tails was eliminated with parity. My argument is different, I would say there is no way to update the probability based on the name because it would involve using self-locating probability. Let's break it down in steps as you suggested. Suppose I ask: "is it true that the coin landed Tails and I'm talking to Peter? " and get a negative answer. You say this would eliminate half the probability for Tails. I say there is no way to say how much probability of Tails is eliminated (because it involves self-locating probability). So we cannot update the probability for this information. You say considering the answer, Tails is reduced to 1/4. I say considering the answer is wrong, if you consider it you get nothing meaningful, no value. Suppose I ask: "is it true that the coin landed Heads and I’m talking to Peter?" and get a negative answer. You say this would eliminate half the probability for Heads making it 1/4. I agree with this. Seeing Bob would effectively be the same as getting two negative answers altogether. How does it combine? You say Heads and Tails both eliminate half the probability (both 1/4 now), so after renormalizing the probability of heads remains unchanged at 1/2. I say since one of the steps is invalid the combined calculation would be invalid too. There is no probability condition on seeing Bob (again because it involves self-locating probability). I suppose your next question would be: if the first question is invalid for updating, wouldn't I just update based on the second question alone? which will give a probability of Heads to 1/3? That is correct as long as I indeed asked the question and got the answer. Like I said before: the long-run frequency for these cases would converge on 1/3. But that is not how the example is set up, i

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

Interesting Dadarren.

I sense that you’re close to being converted to become a ‘pure halfer’, willing to assign probability to self-locations. Let me address what you said.

“Your latter example: after seeing Red/Blue, I will not say Heads' probability is halved while Tails' remain the same. I will say there is no way to update. “

I assume you mean that the probability of 1/2 for Heads or Tails – before and after she sees either colour – remains correct. We... (read more)

1dadadarren3y

Hi Simon, before anything let me say I like this discussion with you- using concrete examples. I find it helps to pinpoint the contention making thinking easier. I think our difference is due to this here: "I assume you mean that the probability of 1/2 for Heads or Tails – before and after she sees either colour – remains correct." Yes and No, but most importantly not in the way you have in mind. Just to quickly reiterate: I argue the first-person perspective is a primitive axiomatic fact. No way to explain or reason. It just is. Therefore no probability. Everything follows from here. It means everything using self-locating probability is invalid. And that includes things like P(Heads|Red). So there is no "probability of Heads given I see a red room". Red cannot be conditioned on because it involves the probability "Now is Tuesday" vs "Now is Monday". Let me follow your steps. If it is Heads then seeing the color is a random event, there is no problem at all, halving the chance is Ok. In the case of Tails, traditional updating would eliminate half the chance too because they give equal probability to Now is Monday vs Now is Tuesday. But because self-locating probability does not exist, there is no basis to split it evenly, or any other way for the matter of fact. There is no valid way to split it at all, that includes a 0-100 split. So what I meant by "there is no way to update" is not saying the correct value of Tails remains unchanged at 1/2. I meant there is no correct value period. And you can't renormalize it with the Heads' chance of 1/4 to get anything. This is why I suggested using the repeatable example with long-run frequencies. It makes the problem clearer. If you follow the first-person perspective of a subject then the long-run frequency of Heads is 1/2. However, the long-run frequency for Red or Blue would not converge to any particular value. And as you suggested, if you are always told if it is Heads and Red, and only counting iterati

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon3y*10

Hi. It's been a while. I still find the implications of your reasoning fascinating. I am seeking to explore whether I agree with it. I recognise there are several double halfer positions. I’ll attempt to work with your version.

For all double halfers, in the original Sleeping Beauty Problem, the probability of Heads is 1/2 before she’s told what day it is and 1/2 after she learn it’s Monday. Whereas for a pure halfer and thirder, the elimination of Tuesday within Tails is subject to Bayesian u... (read more)

1dadadarren3y

Hi Simon. The double-halving argument you are using is different from my approach. It is actually similar to "compartmentalized conditionalization" by Meacham. That argument basically says, for whatever reason, eliminating the case of Tails and Tuesday should not change the probability of Tails as a whole, it only makes Tails and Monday the entire possibility for Tails. i.e. the conditionalization only applies within the "compartment" of Tails. In this case, you used "no self-locating probability" as that reason. If I'm not mistaken this is the earliest form of double-halving argument ever appeared. And it has some problems. Your example is a good counter. My position is that the first-person perspective, such as which person I am, which moment is now, etc, are basic axiomatic facts. Each of us inherently knows which one I am: all experience is due to this physical agent. It is so basic that there is no cause as to why "I am this person", nor is there any explanation to it. It just is. So there is no valid way to think about self-locating probability. No self-locating probability does not mean the probability of Tails remains unchanged at 1/2 after updating, (as compartmentalized conditioning suggested). It means there is no valid way to update using the self-locating information "it is Monday" at all. Because beauty cannot comprehend "the probability that today is Monday". All that can be said is either it is Monday or not and she doesn't know. Yet Bayesian update would have to use probabilities like P(Monday), P(Monday and Heads), P(Monday and Tails), P(Monday|Heads), and P(Monday|Tails) to work. So for your latter example: after seeing Red/Blue, I will not say Heads' probability is halved while Tails' remain the same. I will say there is no way to update. What I find useful while thinking about the paradoxes is to use a repeatable anthropic experiment then use a frequentist approach. Imagine during tonight's sleep, an advanced alien would split yo

A Simplified Version of Perspective Solution to the Sleeping Beauty Problem

Simon4y10

Because you’re a double halfer, I see a contradiction in your conclusion about Lotaria’s colour room example. You’ve previously made a distinction between self-locating events, which are guaranteed to happen, and random outcomes that have genuine probability. Your position has been that rules of conditionalisation apply only to random events, not to self location.

In the colour room example, the coin flips are random events. The subsequently experienced colour ‘blue’ is not... (read more)

4dadadarren4y

The double-halfer logic you just described: not conditionalizing on self-locating information unless it rejects a possible-world (like seeing blue rejects TT in Loaria's example), is called the "halfer rule" by Rachael Briggs. It has obvious shortcomings very well countered by Michael Titelbaum in "An Embarrassment for Double Halfers" and by Vincent Contizer in "A Devastating Example for the Halfer Rule". My position is different from any (double) halfer argument that I know of. I suggest perspectives cannot be reasoned or explained, they are defined by the subjective. So if we want to use "today" as a specific day in the logic, then we have to imagine being the subject waking up in the experiment. Here "today" is a primitively defined moment. Because it is primitive, there is no way to assign any probability to "today is the first day" or "today is the second day". I'm arguing self-locating probabilities like these simply cannot exist. Different from other double-halfer camps that think self-locating probability exists yet try to come up with special updating rules for self-locating information. So there are a few points not consistent with my position. You said experiencing "blue" is not a random event, but I think it is. Imagine waking up during the experiment as the first-person, before checking the color, I understand the time is "today": a moment primitively defined. I do not know the color for today because it depends on today's coin toss: a random event. After seeing Blue I know today's toss is H, but knows nothing about the toss of "the other day". So the probability of both coin having the same result remains at 1/2. If you are interested in my precise position of self-locating probabilities check out my page here. In this analysis whether "today" is the first or the second day was not part of the consideration. However if you really wish to dig into it then here is the analysis: If today is the first then the two possibilities are HT and HH, if today